Step-by-step explanation:
By Pythagoras' Theorem,
we have x² + (x + 2)² = (x + 4)².
=> 2x² + 4x + 4 = x² + 8x + 16
=> x² - 4x - 12 = 0
(The constants are a = -4, b = -12)
=> (x - 6)(x + 2) = 0
=> x = 6 or x = -2
The value x = -2 is rejected as side lengths cannot be negative.
Hence we have x = 6.
=> AB = 6cm, BC = 8cm, AC = 10cm.
P.S. What you see above is the full solution. You just need to type x² - 4x - 12 = 0 in the blank.
